A footnote to a paper by Ionescu
type: Item
instance of: scholarly article
title: A footnote to a paper by Ionescu
zbMATH Open document ID: 0622.14005
DOI: 10.1007/BF00181263
published in: Geometriae Dedicata
publication date: 1987-01-01T00:00:00Z
review text: Let X be a complex projective manifold of dimension \(d\geq 3\), polarized by an ample line bundle H and let \(K_ X\) stand for its canonical bundle. A recent result by \textit{P. Ionescu} [''Generalized adjunction and applications'', Prepr. Ser. Math., Bucuresti 48 (1985)] strongly bounds the dimension of the exceptional locus of the contraction of a non numerically effective extremal ray on X. By using this the ampleness of \(K_ X\otimes H^{d-2W}\) and the semi-ampleness of \(K_ X\otimes H^{d-3} (d\geq 4)\) are studied. Ionescu himself had already described the cases when \(K_ X\otimes H^ t\) is not semi-ample for \(t=d-2, d-1, d\) and is not ample for \(t=d-1, d\). Note also that some of the above results are contained in a recent paper by Fujita. Both Ionescu's paper and Fujita's are quoted in the reference.
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14J40
Mathematics Subject Classification ID: 14J35
zbMATH DE Number: 4008538
zbMATH Keywords: adjoint bundle
zbMATH Keywords: canonical bundle
zbMATH Keywords: dimension of the exceptional locus
zbMATH Keywords: non numerically effective extremal ray
zbMATH Keywords: ampleness
zbMATH Keywords: semi-ampleness
author: Mauro C. Beltrametti
author: Marino Palleschi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4008538